Laws may vary from one country to another, so I can only tell you my personal experience. Therefore, you'll need to investigate what your precise situation is before acting.
I have 2 daughters and now longer with their mother. In the first instance there is a court ruling on the living arrangements. There is primary living arrangement, and secondary. Custody is joint. This means my daughter lives with her mother, and visits me. But neither of us can take important decisions without the agreement of the other. Important decisions include education, operations, emigration and the like. When I applied for a British passport for my daughter, (mother is not British) I did not need to get her to sign. Maybe as you are still married, it is different.
In the case of my youngest there is no court ruling, but automatically it is joint. Whether this is just for Germany, or because we are not married, or EU ruling, I don't know - worth checking.
It may be as you are not yet divorced, you automatically have joint. Really need to check - also concerning who left the family home etc etc.